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The Thermal Conductivity

Thermal conductivity measures a material's ability to transmit heat through conduction. It is defined by Fourier's law as the ratio of heat flux to the temperature gradient across a material. The transient hot wire method is used to measure the low thermal conductivity of liquids. It works by detecting the temporal temperature rise in a thin wire immersed in a liquid following the application of an electrical current. By analyzing the temperature rise over time, the thermal conductivity of the liquid can be derived from the slope of the logarithmic temperature plot.

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Luc Le
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87 views

The Thermal Conductivity

Thermal conductivity measures a material's ability to transmit heat through conduction. It is defined by Fourier's law as the ratio of heat flux to the temperature gradient across a material. The transient hot wire method is used to measure the low thermal conductivity of liquids. It works by detecting the temporal temperature rise in a thin wire immersed in a liquid following the application of an electrical current. By analyzing the temperature rise over time, the thermal conductivity of the liquid can be derived from the slope of the logarithmic temperature plot.

Uploaded by

Luc Le
Copyright
© © All Rights Reserved
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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The thermal conductivity, as defined by Fouriers equation, is a materials ability to transmit heat

by means of conduction, which allows the flow of heat from its warmer surface through the material to
its colder surface shown in Figure ### below:

Figure ###: The illustration for measurement the thermal conductivity of an object.
Thermal conductivity is measured in watts per kelvin-meter (WK 1m1, i.e. W/(Km) or in IP
units (Btuhr1ft1F1, i.e. Btu/(hrftF). From the Fourier equation, the thermal conductivity of
material is defined as in Eq ###
k=

Q/ A
T / L

(###)

where Q is the amount of heat transferring through a cross section area of material (A) that
causes a temperature difference ( T over a distance ( L ). The main difficulty of
measuring thermal conductivity of a liquid is to measure the heat flux (Q/A) because liquid is
subjected to the flow motion of its molecules and does not have a well-defined area.
Consequently, the heat transfer source is not pure conduction, but it is combination of
conduction, convection or even radiation. The value of thermal conductivity is a material related
property, which is dependent on pressure and temperature. However, in most cases temperature
has higher magnitude effect on thermal conductivity of material than pressure. For solid
materials over certain temperature ranges, thermal conductivity is small enough to be neglected.
However, in many cases, such as liquids and gases, the variation of the thermal conductivity with
temperature is significant.
Depending on the thermal properties of material and the medium temperature, there are two
broad categories of measuring thermal conductivity of material: steady-state and transient state.
The steady state technique is used to measure material that has high thermal conductivity such as
solid, while the transient state technique is used to measure material that has low thermal
conductivity such as liquid. In this experiment, we use the transient hot wire technique for
measurement of the thermal conductivity of liquid. It woks based on the detection of the

temporal temperature rise in a thin wire immersed in the tested liquid, initially at thermal
equilibrium, following the application of a stepwise electrical current. The wire acts as a heat
source and produces a time-dependent temperature field within the liquid. The temperature rise
at the radial distance r from the heat source is given by

T (r , t)=

Q
r2
ln
+ ln ( t )
4 k
4a

( )

where Q is the total heat, k is thermal conductivity (WK1m1), a is thermal diffusivity of


tested fluid (m2s-1) and is a Eulers constant 0.5772157. The plot of the temperature T(r,t) on a
logarithmic scale of time, ln(t), is linear, with the slope m=Q/(4k), from that the thermal
conductivity can be derived as Eq. ### below:
k=

Q
4 m

MF

Name

-25 C

0C

25 C 50 C 75 C 100 C

Cl 4 Si

Silicon tetrachloride

H2O

Water

Hg

Mercury

7.25

7.77

8.25

8.68

9.07

9.43

CCl 4

Tetrachloromethane

0.104

0.099

0.093

0.088

CS 2

Carbon disulfide

0.154

0.149

CHCl 3

Trichloromethane

0.127

0.122

0.117

0.112

0.107

0.102

CH 2 Br 2

Dibromomethane

0.120

0.114

0.108

0.103

0.097

CH 4 O

Methanol

0.214

0.207

0.200

0.193

C 2 Cl 4

Tetrachloroethylene

0.117

0.110

0.104

0.097

0.091

C 2 HCl 3

Trichloroethylene

0.133

0.124

0.116

0.108

0.100

C 2 H 3 Cl 3

1,1,1-Trichloroethane

0.106

0.101

0.096

C2H3N

Acetonitrile

0.208

0.198

0.188

0.178

0.168

0.099

0.096

0.5610 0.6071 0.6435 0.6668 0.6791

C2H4O2

Acetic acid

0.158

0.153

0.149

0.144

C 2 H 5 Cl

Chloroethane

0.145

0.132

0.119

0.106

0.093

C 2 H 5 NO

N -Methylformamide

0.203

0.201

0.199

0.196

C2H6O

Ethanol

0.176

0.169

0.162

C2H6O2

Ethylene glycol

0.256

0.256

0.256

0.256

0.256

C 2 H 7 NO

Ethanolamine

0.299

0.286

0.274

0.261

C 3 H 5 ClO

Epichlorohydrin

0.142

0.137

0.131

0.125

0.119

0.114

C3H6O

Acetone

0.169

0.161

C3H6O2

Methyl acetate

0.174

0.164

0.153

0.143

0.133

0.122

C 3 H 7 NO

N,N -Dimethylformamide

0.184

0.178

0.171

0.165

C3H8O

1-Propanol

0.162

0.158

0.154

0.149

0.145

0.141

C3H8O

2-Propanol

0.146

0.141

0.135

0.129

0.124

0.118

C3H8O2

1,2-Propanediol

0.202

0.200

0.199

0.198

0.197

C3H8O3

Glycerol

0.292

0.295

0.297

0.300

C3H9N

Trimethylamine

0.143

0.133

C4H4O

Furan

0.142

0.134

0.126

C4H4S

Thiophene

0.199

0.195

0.191

0.186

C4H6

2-Butyne

0.137

0.129

0.121

C4H8O

2-Butanone

0.158

0.151

0.145

0.139

0.133

C 4H 8 O

Tetrahydrofuran

0.132

0.126

0.120

0.114

C4H8O2

1,4-Dioxane

0.159

0.147

0.135

0.123

C4H8O2

Ethyl acetate

0.162

0.153

0.144

0.135

0.126

C 4 H 10 O

1-Butanol

0.158

0.154

0.149

C 4 H 10 O

Diethyl ether

0.150

0.140

0.130

0.120

0.110

0.100

C5H5N

Pyridine

0.169

0.165

0.161

0.158

C5H8

Cyclopentene

0.143

0.136

0.129

C 5 H 10

1-Pentene

0.131

0.124

0.116

C 5 H 10

Cyclopentane

0.140

0.133

0.126

C 5 H 12

Pentane

0.132

0.122

0.113

0.103

0.095

0.087

C 5 H 12 O

1-Pentanol

0.157

0.153

0.149

0.145

C 6 H 5 Cl

Chlorobenzene

0.136

0.131

0.127

0.122

0.117

0.112

For reference
http://www.engineersedge.com/heat_transfer/thermal_conductivity_of_liquids_9921.
htm
http://www.imt.ro/romjist/Volum10/Number10_3/pdf/01-Codreanu.pdf
http://www.eurotherm2008.tue.nl/Proceedings_Eurotherm2008/papers/Conduction/C
ON_10.pdf
http://www.imeko.org/publications/wc-2003/PWC-2003-TC12-027.pdf
The theoretical model describing the THW technique is derived from the analytical solution of
the heat conduction equation for a line heat source of radius r!0 and lengthl!1 of negligible
thermal mass, which is perfectly embedded, with no thermal contact resistance, in an unbounded
heat sink, initially at uniform temperature T0. The sink is considered of homogeneous and
isotropic material with constant thermal transport properties. When a constant electric power is
stepwise applied, the wire instantly and totally liberates the heat source output per unit length, to
the test sample, where it is conducted outwards and stored entirely.

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